Tech support issue…

I want to preface this by saying that I am NOT asking how to fix my computer, or for legal advice. Instead I'm wondering how far you would go wtih an expensive piece of shit equipment.
Background
I bought a laptop for around 1400 dollars from a semi well known electronics manufacturer last September. It worked fine for the most part, but last June, the backlight from the screen started sporatically failling. I called tech support, and they determined it was a hardware problem. (at this point I simply hooked it up to my old monitor and used it, although it defeated the purpose of purchasing a lap top) I was given the choice of mailing it and being computer-less for 3 weeks, or driving it an hour and leaving it for a week, driving back to the place, and picking it up. I chose the latter, and the nice technician not only "fixed" my monitor, but replaced some parts that needed replacing since it was still under warranty. So around the 21st, i got my computer back and all was well.
Until Wednesday, when the SAME backlight problem occurred. I don't do anything to the computer. It sits on my desk 80% of the time, and I have a padded bag for it and everything. I don't drop it or spill things on it. I take SUPER good care of it 'cause I don't have money to buy a new one. My old computer was made of more parts, and I made it last for 4 years even though it only had 64 megs of ram and no speakers. My computer-loving friends always commented on the great shape in which I kept that piece of junki! I called tech support AGAIN and they told me to take it to the repair place (there's only two in my area) AGAIN or mail it in. I had several problems:
1)Will they even fix it right, or will the simply string me along until my Warranty is out?
2) School started this week. I need my computer.
3) Why should I drive an hour when their technician messed up? I asked them if I could take my computer to Best Buy or something by me and get reimbursed for the repairs. They said no.
4) I'm REALLY concerned that this will keep happening, and my warranty is up in September
So how much should I push this issue? I want them to replace the computer. I paid good money for a laptop, and I should not worry about taking it places because it will lose the screen. At the very least, I would like them to allow me to get it fixed by someone else that might fix it RIGHT. If I keep this computer, I think they should give me an extra year in warranty. Am I unreasonable? This was a HUGE purchase for me, and I need it to last for at least another 4 or 5 years, which is why I got a computer this "nice". I researched it, and it sounded good, and I got a great deal on it (almost 500 dollars in rebates). This is the only expensive thing I own, so I'm not sure what I should expect from the company.
Edit: It's a Toshiba.